Gaussian Process Boosting

We introduce a novel way to combine boosting with Gaussian process and mixed effects models. This allows for relaxing, first, the linearity assumption for the mean function in Gaussian process and grouped random effects models in a flexible non-parametric way and, second, the independence assumption made in most boosting algorithms. The former is advantageous for predictive accuracy and for avoiding model misspecifications. The latter is important for more efficient learning of the mean function and for obtaining probabilistic predictions. In addition, we present an extension that scales to large data using a Vecchia approximation for the Gaussian process model relying on novel results for covariance parameter inference. We obtain increased predictive accuracy compared to existing approaches on several simulated and real-world data sets.